Sunday, 24 March 2013

NB: This post is a redux of a previous discussion on the same topic. The difference this time is more reasoning behind the stats and me asking the opinions of other people. Therefore the updated results address suggestions and challenges from a few people, including Alex Hutchinson himself. I feel the questions if not satisfactorily answered are at least out in the open. The good news is that my "discovery" appears to have survived the most obvious challenges and the conclusions should now be more robust.

I wanted to find out what sort of trends, if any, appeared when taking the ratios between the top (i.e. fastest) men's and top women's ratio of times in two sports: swimming and running. I define a ratio as the following

Ratio = [Time for a woman to complete distance X]/[Time for a man to complete distance X]

For example, if considering the 10,000 m track event and a woman's time is 32 minutes while a man's is 29 flat, their time ratio is 32:00/29:00 = 1.10. Let's then take another fictitious ratio of 1500m times as 4:20(female)/3:59(male) = 1.08.

Why go to the trouble taking these ratios? To skip ahead, what I've found is that as distance X increases, this ratio goes up for running and down for swimming. Using the same two examples as above, the fictitious ratio goes up from 1.08 to 1.10 as I increase X from 1.5 km to 10km. Here my argument holds because I invented the numbers. All numbers from this point onward will be quite real. Below is an illustration of what I will soon show with actual data:

Simple enough to do these calculations, however it turned out to be more difficult arguing there was any inherent meaning the final results. Considering the above example yet again, I what have I actually shown? Another faster male might run the 1500m in 3:50, so the new ratio becomes 1.13 and my argument now falls to pieces. Or the female times are artificially slow due to low participation. Clearly I am going to need a lot of evidence to support such a sweeping generalization as "women improve with respect to men in swimming but worsen for running". From a (admittedly cursory) check with the available literature and a couple of correspondences, I have not seen these two trends discussed together. Even if the swimming/running down/up trend is well-known, it was a good exercise working with different lines of reasoning. And I imagine at least some of the data here could somehow be novel.